The emerging field of canine cognitive neuroscience uses neuroimaging tools such as electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) to map the cognitive processes of dogs to neural substrates in their brain. Within the past decade, the non-invasive use of EEG has provided real-time, accessible, and portable neuroimaging insight into canine cognitive processes. To promote systematization and create an overview of framings, methods and findings for future work, we provide a systematic review of non-invasive canine EEG studies (N=22), dissecting their study makeup, technical setup, and analysis frameworks and highlighting emerging trends. We further propose new directions of development, such as the standardization of data structures and integrating predictive modeling with descriptive statistical approaches. Our review ends by underscoring the advances and advantages of EEG-based canine cognitive neuroscience and the potential for accessible canine neuroimaging to inform both fundamental sciences as well as practical applications for cognitive neuroscience, working dogs, and human-canine interactions.